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Dergiler / Turkish Journal of Mathematics / 2019 / Cilt: 43 - Sayı: 6

A variational study on a natural Hamiltonian for curves

Gözde ÖZKAN TÜKEL
Sayfa
2931–2940
Yayın Tarihi
2022-11-03
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

Finally, the problem isgeneralized to finding extremals of total squared torsion functional for nonnull curves in Minkowski 3−space.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:A variational study of finding critical points of the total squared torsion functional for curves in Euclidean3−spaces is presented.
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Temel Bulgular & Veri:Critical points of this functional also known as one of the natural Hamiltonians of curves arecharacterized by two Euler−Lagrange equations in terms of curvature and torsion of a curve.
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Sonuç & Katkı:Finally, the problem isgeneralized to finding extremals of total squared torsion functional for nonnull curves in Minkowski 3−space.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

A variational study of finding critical points of the total squared torsion functional for curves in Euclidean3−spaces is presented. Critical points of this functional also known as one of the natural Hamiltonians of curves arecharacterized by two Euler−Lagrange equations in terms of curvature and torsion of a curve. To solve these balanceequations, the curvature of the critical curve is expressed by its torsion so that equations are completely solved byquadratures. Then two Killing fields along the critical curve are found for integrating the structural equations of thecritical curve and this curve is expressed by quadratures in a system of cylindrical coordinate. Finally, the problem isgeneralized to finding extremals of total squared torsion functional for nonnull curves in Minkowski 3−space.

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Bu Makaleye Atıf Yap

TÜKEL, G. Ö. (2022). A variational study on a natural Hamiltonian for curves. Turkish Journal of Mathematics, Cilt: 43 - Sayı: 6, 2931–2940. https://ajindex.com/articles/608077

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Kaynakça (16)

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